We report on the behavior of the ionization avalanche in an ensemble of ultracold 87Rb atoms coupled to a high-lying Rydberg state and investigate extensions to the current model by including the effects of three-body recombination and plasma expansion. To separate the two effects we study the time dependence of the plasma formation at various densities as well as for different nS and nD states. At medium densities and low n we observe the onset of the avalanche as has been reported in other experiments, as well as a subsequent turn-off of the avalanche for longer excitation times, which we associate with plasma expansion. At higher densities and for higher-lying Rydberg states we observe a disappearance of the avalanche signature, which we attribute to three-body recombination.